PH5023 Monte Carlo Radiation Transport Techniques

Kenny Wood (kw25)

Overview

This module introduces the theory and practice behind Monte Carlo radiation transport codes for use in physics, astrophysics, atmospheric physics, neutron transport for criticality calculations, and medical physics. Core topics that will be covered include: recap of basic radiation transfer; techniques for sampling from probability distribution functions; an isotropic scattering code; computing the radiation field, pressure, temperature, and ionisation structure; programming skills required to write Monte Carlo codes; code speed-up techniques and parallel computing; three-dimensional codes.

The module will comprise lectures and at least two taught lab sessions. The lecture notes will be provided on-line below both in PDF format and read-only pptx files with audio. The lab sessions will introduce the basic Fortran programming skills required for the module. By the end of the lab sessions each student will have written their own Monte Carlo codes to sample from probability distribution functions and also a code that simulates isotropic scattering of radiation from a point source at the centre of a unifom density sphere. Another lab session will follow on from lectures that describe a publicly available three dimensional scattering code. During this lab session, students will be led through the 3D code's subroutines and how to adapt them for their own three dimensional radiation transport simulations.

Prerequsites: PH2012: Physics 2B, plus at least 1 of the following: AS3013: Computational Astrophysics, PH3080: Computational Physics, PH3081: Mathematics for Physicists, PH3082: Mathematics for Chemistry/Physics

Texbooks

A Monte Carlo Primer by Dupree & Fraley. This book focuses on neutron transport but the techniques are the same for photon transport and it has lots of programming examples. Several copies of this have been bought for the Physics & Astronomy library.

Steve Jacques (who gave three guest lectures in 2014) has supplied this review chapter on Monte Carlo simulations of photon transport in biological tissue: PDF

Lectures

PDFs of the lecture slides are available with two slides per page. The Power Point files containing audio on each slide are available as read-only pptx files.

Monte Carlo Radiation Transport on a 3D Cartesian Grid

I have set up a 3D grid code to compute the average number of scatterings of photons emitted from the centre of a uniform density sphere. The emission and scattering are both assumed to be isotropic. The code algorithms and subroutines are described in the lecture "MCRT on a 3D Cartesian Grid." You can download a tar file of the code here. To unpack the tarball, type "tar - xvf grid.tar" and this will give you eight fortran files, two txt files, an input.params file, a README, and a Makefile. To get started type "make" and this will produce an executable file called "mcgrid." When you run this the code will generate some output to the screen. The code is set up for a simulation where the optical depth across the sphere's diameter is 20 (radial optical depth of 10). The average number of scatterings for this optical depth and input parameters given is 57.35.

The code writes out a file "density.dat" which is an unformatted fortran file comprising the 3D density grid. You may use this short fortran code, read_write.f to read in the density grid and write out a 2D slice through the grid. You can then import the output 2D slice into a plotting program (gnuplot, IDL, Mathematica, etc) to display the slice as a 2D image.

Resources

Here are some links to texts and other Monte Carlo lectures and courses that I've found on random walks around the internet...

Texts, Notes, and Review Chapters:
The classic text by Cashwell and Everett (1957): A Practical Manual on the Monte Carlo Method for Random Walk Problems PDF
Monte Carlo Techniques of Electron and Photon Transport for Radiation Dosimetry by Rogers and Bielajew PDF

Historical development of Monte Carlo Radiation Transfer
The following files are from the Los Alamos archive and give a very enjoyable overview of the development of MCRT.
Letter from John von Neumann to Bob Richtmyer, 1947
The Beginning of the Monte Carlo Method by Nick Metropolis
Stan Ulam, John von Neumann, and the Monte Carlo Method, by Roger Eckhardt
Metroplois, Monte Carlo, and the MANIAC, by H.L. Anderson

Lecture Courses and Summer Schools
St Andrews Monte Carlo Summer School